This time of year really shows up old/worn rubber, so what we might've been getting away with in the Summer could bite you on the bum in Winter. Obviously nowadays a lot of folks change to specific Winter tyres (I've never done this as I do low miles all year round and feel OK on my 'normal' tyres - Michelin Pilots with good tread depth). The current combo of colder temps and salty/greasy roads is dodgy with 'good' tyres, but if they're pretty worn I'd seriously think about replacing them. As others have said, it's expensive but cheaper than dumping it in a ditch... Roundabouts are the worst as you often get a bit of diesel from over-filled lorries etc, when even good tyres lose it.

Going on a Winter NMS run a few years back finally made up my mind to get rid of my hard runflats, as I was sh****ng myself on the corners! A graphic illustration of how important suitable/good tyres are.